<PAGE>   1
 
================================================================================
 
                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549
 
                            ------------------------
 
                                   FORM 10-Q
 
(MARK ONE)
      [X]        QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
 
               FOR THE QUARTERLY PERIOD ENDED SEPTEMBER 30, 1997
 
                                       OR
 
      [  ]       TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d)
                     OF THE SECURITIES EXCHANGE ACT OF 1934
 
                        COMMISSION FILE NUMBER: 0-22967
 
                            NETWORK SOLUTIONS, INC.
             (Exact name of registrant as specified in its charter)
 
<TABLE>
<S>                                            <C>
                   DELAWARE                                      52-1146119
         (State or other jurisdiction                         (I.R.S. Employer
       of incorporation or organization)                     Identification No.)
</TABLE>
 
                             505 HUNTMAR PARK DRIVE
                            HERNDON, VIRGINIA 20170
                                 (703) 742-0400
              (Address, including zip code, and telephone number,
       including area code, of Registrant's principal executive offices)
 
     Indicate by check mark whether the Registrant (1) has filed all reports
required to be filed by Section 13 or 15(d) of the Securities Exchange Act of
1934 during the preceding 12 months (or for such shorter period that the
Registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days.
 
                         (1)  Yes   X          No  
                                   ---             ---
                         (2)  Yes              No   X
                                   ---             ---
 
     As of October 31, 1997, the Registrant had 3,795,000 shares of Class A
common stock, $0.001 par value per share, issued and outstanding, and 11,925,000
shares of Class B common stock, $0.001 par value per share, issued and
outstanding.
 
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<PAGE>   2
 
<TABLE>
<CAPTION>
                                                                                          PAGE
                                                                                          ----
<S>        <C>                                                                            <C>
PART I     FINANCIAL INFORMATION
 
Item 1.    Financial Statements
           Statements of Financial Position as of December 31, 1996 and
             September 30, 1997 (unaudited)............................................     3
           Unaudited Statements of Operations for the three and nine months ended
             September 30, 1996 and 1997...............................................     4
           Unaudited Statements of Changes in Stockholder's Equity for the
             nine months ended September 30, 1997......................................     5
           Unaudited Statements of Cash Flows for the nine months ended
             September 30, 1996 and 1997...............................................     6
           Notes to Financial Statements...............................................     7
 
Item 2.    Management's Discussion and Analysis of Financial Condition and
             Results of Operations.....................................................     9
 
Item 3.    Quantitative and Qualitative Disclosures About Market Risk..................    12
 
PART II    OTHER INFORMATION
Item 1.    Legal Proceedings...........................................................    12
Item 2.    Changes in Securities and Use of Proceeds...................................    13
Item 6.    Exhibits....................................................................    14
Signature..............................................................................    15
Index to Exhibits......................................................................    16
</TABLE>
<PAGE>   3
 
PART I FINANCIAL INFORMATION
 
ITEM 1. FINANCIAL STATEMENTS.
 
                            NETWORK SOLUTIONS, INC.
 
                        STATEMENTS OF FINANCIAL POSITION
 
<TABLE>
<CAPTION>
                                                                                     
                                                                     DECEMBER 31,    SEPTEMBER 30, 
                                                                         1996            1997      
                                                                     ------------    ------------- 
                                                                                      (UNAUDITED)
<S>                                                                  <C>             <C>
ASSETS
Current assets:
  Cash and cash equivalents.......................................   $15,540,000     $  19,062,000
  Short-term investments..........................................            --        28,321,000
  Accounts receivable, net........................................    12,587,000         6,662,000
  Prepaids and other assets.......................................       936,000         1,832,000
  Restricted assets...............................................    17,453,000        40,135,000
  Deferred tax asset..............................................    10,087,000        17,350,000
                                                                     ------------    -------------
Total current assets..............................................    56,603,000       113,362,000
Furniture and equipment, net......................................     2,266,000         4,812,000
Deferred tax asset................................................     4,968,000         7,354,000
Goodwill, net.....................................................     2,281,000         1,740,000
                                                                     ------------    -------------
Total Assets......................................................   $66,118,000     $ 127,268,000
                                                                     ===========     =============
LIABILITIES AND STOCKHOLDER'S EQUITY
Current liabilities:
  Accounts payable and accrued liabilities........................   $ 2,581,000     $   4,392,000
  Dividend payable................................................            --        10,000,000
  Due to parent...................................................    15,295,000        21,922,000
  Deferred revenue, net...........................................    19,912,000        38,281,000
  Current portion of capital lease obligations....................            --         1,284,000
  Internet fund liability.........................................    17,453,000        40,135,000
                                                                     ------------    -------------
Total current liabilities.........................................    55,241,000       116,014,000
Capital lease obligations.........................................            --         1,102,000
Long-term deferred revenue, net...................................     9,440,000        16,227,000
                                                                     ------------    -------------
Total liabilities.................................................    64,681,000       133,343,000
Stockholder's equity:
  Preferred stock, $.001 par value, authorized 10,000,000 shares;
     none issued and outstanding in 1996 and 1997.................
  Class A common stock, $.001 par; authorized 100,000,000 shares;
     none issued and outstanding..................................
  Class B common stock, $.001 par; authorized 30,000,000 shares;
     12,500,000 issued and outstanding............................        12,000            12,000
  Additional paid-in capital......................................     4,468,000         4,468,000
  Accumulated deficit.............................................    (3,043,000)      (10,555,000)
                                                                     ------------    -------------
Total stockholder's equity........................................     1,437,000        (6,075,000)
Commitments and contingencies
                                                                     ------------    -------------
Total Liabilities and Stockholder's Equity........................   $66,118,000     $ 127,268,000
                                                                     ===========     =============
</TABLE>
 
   The accompanying notes are an integral part of these financial statements.
 
                                        3
<PAGE>   4
 
                            NETWORK SOLUTIONS, INC.
 
                            STATEMENTS OF OPERATIONS
                                  (UNAUDITED)
 
<TABLE>
<CAPTION>
                                                 THREE MONTHS ENDED            NINE MONTHS ENDED
                                                   SEPTEMBER 30,                 SEPTEMBER 30,
                                             --------------------------    --------------------------
                                                1996           1997           1996           1997
                                             -----------    -----------    -----------    -----------
<S>                                          <C>            <C>            <C>            <C>
Net revenue...............................   $ 5,180,000    $12,172,000    $12,009,000    $30,896,000
Cost of revenue...........................     3,719,000      7,033,000     10,240,000     18,468,000
                                             -----------    -----------    -----------    -----------
Gross profit..............................     1,461,000      5,139,000      1,769,000     12,428,000
Research and development expenses.........       226,000        377,000        284,000      1,095,000
Selling, general and
  administrative expenses.................     1,932,000      3,105,000      4,302,000      7,893,000
Interest income, net......................      (288,000)      (570,000)      (374,000)    (1,054,000)
                                             -----------    -----------    -----------    -----------
Income (loss) before income taxes.........      (409,000)     2,227,000     (2,443,000)     4,494,000
Provision (benefit) for income taxes......      (116,000)       995,000       (692,000)     2,006,000
                                             -----------    -----------    -----------    -----------
Net income (loss).........................   $  (293,000)   $ 1,232,000    $(1,751,000)   $ 2,488,000
                                             ===========    ===========    ===========    ===========
Pro forma net income (loss) per share.....   $     (0.02)   $      0.09    $     (0.13)   $      0.19
                                             ===========    ===========    ===========    ===========
Shares used in computing pro forma net
  income (loss) per share.................    13,487,000     13,161,000     13,487,000     13,373,000
                                             ===========    ===========    ===========    ===========
</TABLE>
 
   The accompanying notes are an integral part of these financial statements.
 
                                        4
<PAGE>   5
 
                            NETWORK SOLUTIONS, INC.
 
                 STATEMENTS OF CHANGES IN STOCKHOLDER'S EQUITY
                                  (UNAUDITED)
 
<TABLE>
<CAPTION>
                                           CLASS B
                                        COMMON STOCK         ADDITIONAL      RETAINED          TOTAL
                                    ---------------------     PAID-IN        EARNINGS      STOCKHOLDER'S
                                      SHARES      AMOUNT      CAPITAL       (DEFICIT)         EQUITY
                                    ----------    -------    ----------    ------------    -------------
<S>                                 <C>           <C>        <C>           <C>             <C>
Balance, December 31, 1996.......   12,500,000    $12,000    $4,468,000    $ (3,043,000)   $   1,437,000
Net income for the nine months
  ended September 30, 1997.......                                             2,488,000        2,488,000
Declaration of Class B
  dividend.......................                                           (10,000,000)     (10,000,000)
                                    ----------    -------    ----------    ------------    -------------
Balance, September 30, 1997......   12,500,000    $12,000    $4,468,000    $(10,555,000)   $  (6,075,000)
                                    ==========    =======    ==========    ============    =============
</TABLE>
 
   The accompanying notes are an integral part of these financial statements.
 
                                        5
<PAGE>   6
 
                            NETWORK SOLUTIONS, INC.
 
                            STATEMENTS OF CASH FLOWS
                                  (UNAUDITED)
 
<TABLE>
<CAPTION>
                                                                          NINE MONTHS ENDED
                                                                            SEPTEMBER 30,
                                                                     ---------------------------
                                                                         1996           1997
                                                                     ------------    -----------
<S>                                                                  <C>             <C>
CASH FLOWS FROM OPERATING ACTIVITIES:
  Net income (loss)...............................................   $ (1,751,000)   $ 2,488,000
  Adjustments to reconcile net income (loss) to net cash provided
     by (used in) operating activities:
     Depreciation and amortization................................        768,000      1,635,000
     Provision for uncollectible accounts receivable..............      2,677,000      5,577,000
     Deferred income taxes........................................    (10,282,000)    (9,649,000)
     Change in operating assets and liabilities:
       Decrease (increase) in accounts receivable.................    (14,062,000)       348,000
       Increase in prepaid and other assets.......................       (466,000)      (896,000)
       Increase in accounts payable and accrued liabilities.......      1,190,000      1,811,000
       Increase in deferred revenue...............................     18,665,000     25,156,000
                                                                     ------------    -----------
          Net cash provided by (used in) operating activities.....     (3,261,000)    26,470,000
                                                                     ------------    -----------
CASH FLOWS FROM INVESTING ACTIVITIES:
  Purchase of furniture and equipment.............................     (1,844,000)    (1,254,000)
  Purchase of short-term investments, net.........................             --    (28,321,000)
  Net investment in net assets of discontinued operations.........       (208,000)            --
                                                                     ------------    -----------
          Net cash used in investing activities...................     (2,052,000)   (29,575,000)
                                                                     ------------    -----------
CASH FLOWS FROM FINANCING ACTIVITIES:
  Net transactions with SAIC......................................      7,298,000      6,627,000
                                                                     ------------    -----------
          Net cash provided by financing activities...............      7,298,000      6,627,000
                                                                     ------------    -----------
Net increase in cash and cash equivalents.........................      1,985,000      3,522,000
Cash and cash equivalents, beginning of period....................          5,000     15,540,000
                                                                     ------------    -----------
Cash and cash equivalents, end of period..........................   $  1,990,000    $19,062,000
                                                                     ============    ===========
</TABLE>
 
   The accompanying notes are an integral part of these financial statements.
 
                                        6
<PAGE>   7
 
                            NETWORK SOLUTIONS, INC.
 
                         NOTES TO FINANCIAL STATEMENTS
 
NOTE 1 -- ORGANIZATION AND BUSINESS
 
     Network Solutions, Inc. (the Company) was incorporated in the District of
Columbia in 1979 and was reincorporated in Delaware in 1996. The Company
currently acts as the exclusive registrar of Internet domain names within the
 .com, .org, .net and .edu top level domains (TLDs) pursuant to a Cooperative
Agreement with the National Science Foundation (NSF). The Company also provides
Intranet consulting and network design and implementation services to large
companies that desire to establish or enhance their Internet presence or to
"re-engineer" legacy network infrastructures to accommodate the integration of
both Internet connectivity and Intranet network technology into their
information technology base.
 
NOTE 2 -- SIGNIFICANT ACCOUNTING POLICIES
 
INTERIM FINANCIAL STATEMENTS
 
     The interim financial statements have been prepared by the Company, without
audit, pursuant to the rules and regulations of the Securities and Exchange
Commission. In the opinion of management, financial statements included in this
report reflect all normal recurring adjustments which the Company considers
necessary for fair presentation of the results of operations for the interim
periods covered and of the financial position of the Company at the date of the
interim balance sheet. Certain information and footnote disclosures normally
included in the annual financial statements prepared in accordance with
generally accepted accounting principles have been condensed or omitted pursuant
to such rules and regulations. However, the Company believes that the
disclosures are adequate for understanding the information presented. The
operating results for interim periods are not necessarily indicative of the
operating results for the entire year. These interim financial statements should
be read in conjunction with the Company's Form S-1 Registration Statement
declared effective on September 25, 1997.
 
NOTE 3 -- INITIAL PUBLIC OFFERING
 
     On October 1, 1997, the Company completed an initial public offering (the
"IPO") of 3,795,000 shares of its $.001 par value Class A common stock,
including 495,000 shares resulting from the exercise of certain overallotment
provisions. The Company's proceeds from the IPO, including overallotment, were
$54 million based on the direct sale of 3,220,000 shares of Class A common
stock. This transaction is not reflected in the interim financial statements
dated as of September 30, 1997.
 
     Prior to the offering, the Company was a wholly-owned subsidiary of Science
Applications International Corporation, a Delaware corporation ("SAIC"). In
conjunction with the IPO, SAIC converted 575,000 shares (including 75,000
overallotment shares) of Class B common stock into 575,000 shares Class A common
stock and directly sold the shares as a selling stockholder. Upon completion of
the offering, SAIC owns 100% of the outstanding Class B common stock
representing 75.9% of the Company's equity and 96.9% of the combined voting
power of the Company's outstanding Class B and Class A common stock.
 
NOTE 4 -- DIVIDEND
 
     On August 21, 1997, the Board of Directors declared a $10,000,000 dividend
to be paid to SAIC upon consummation of the IPO. This dividend was paid to SAIC
on October 1, 1997.
 
                                        7
<PAGE>   8
 
                            NETWORK SOLUTIONS, INC.
 
                   NOTES TO FINANCIAL STATEMENTS--(CONTINUED)
 
NOTE 5 -- COMPUTATION OF PRO FORMA NET INCOME (LOSS) PER SHARE
 
     Pro forma net income (loss) per share is computed using the pro forma
weighted average number of common and common equivalent shares outstanding. Pro
forma weighted average common and common equivalent shares include common stock
and stock options using the treasury stock method.
 
     Pursuant to the requirements of the Securities and Exchange Commission,
common stock and stock options issued by the Company during the twelve months
immediately preceding the filing of the initial registration statement and
through the effective date of such registration statement have been included in
the calculation of the pro forma weighted average shares outstanding using the
treasury stock method based on the IPO price. Additionally, as required by the
Securities and Exchange Commission, the pro forma per share data presented
treats as outstanding for purposes of the calculation the number of shares from
the public offering necessary to fund the amount of the $10,000,000 dividend
payable to SAIC in excess of the Company's net income for the twelve months
ended June 30, 1997.
 
     The Company will adopt Statement of Financial Accounting Standards No. 128,
"Earnings Per Share" ("FAS 128") in the fourth quarter of 1997, as required. The
Company will continue to apply Accounting Principles Board Opinion No. 15,
"Earnings Per Share" ("APB 15") until the adoption of FAS 128. Based on a
preliminary evaluation of FAS 128, the Company does not expect the per share
amounts reported under FAS 128 to be materially different from those calculated
and presented under APB 15.
 
                                        8
<PAGE>   9
 
ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
OF OPERATIONS.
 
OVERVIEW
 
     This Quarterly Report on Form 10-Q contains forward-looking statements. For
this purpose, any statements contained herein that are not statements of
historical fact may be deemed to be forward-looking statements. Statements
regarding the intent, belief or current expectations of the Company are intended
to be forward-looking statements which may involve risk and uncertainty. There
are a number of factors that could cause the Company's actual results to differ
materially from those indicated by such forward-looking statements, including,
but not limited to, those discussed in the Company's Form S-1 Registration
Statement as declared effective by the Securities and Exchange Commission on
September 25, 1997 and incorporated herein by reference.
 
RESULTS OF OPERATIONS
 
     Net Revenue.  Net revenue increased 135% from $5.2 million for the three
months ended September 30, 1996 to $12.2 million for the three months ended
September 30, 1997. This increase in net revenue was primarily attributable to
the increase in the number of domain name subscriptions, principally in the .com
TLD. Subscription growth has been driven by the widespread use and adoption by
businesses of the Internet and Intranets on a global basis. Net revenue from
registration services increased 215% from $3.4 million for the three months
ended September 30, 1996 to $10.7 million for the three months ended September
30, 1997. The provision for uncollectible accounts used in determining net
registration revenue for the three months ended September 30, 1996 and 1997 was
consistently applied at a rate of 30%. Net registrations increased 112% from
121,000 for the three months ended September 30, 1996 to 256,000 for the three
months ended September 30, 1997. Cumulative net registrations as of September
30, 1996 were 461,000 as compared to 1,296,000 as of September 30, 1997.
 
     Net revenue from Intranet services decreased 17% from $1.8 million for the
three months ended September 30, 1996 to $1.5 million for the three months ended
September 30, 1997. This decrease was primarily attributable to a decrease in
business from NationsBanc Services, Inc. ("NationsBanc"). NationsBanc, the
Company's largest Intranet services client, accounted for $904,000 or 17.5% of
the Company's total net revenue for the three months ended September 30, 1996
and $305,000 or 2.5% of the Company's total net revenue for the three months
ended September 30, 1997. During the first quarter of 1997, task orders for a
number of services that the Company had historically performed for NationsBanc
were not renewed. Though these actions will have an impact on the Company's
Intranet services revenue for the balance of 1997, the Company believes
NationsBanc will continue to be a significant customer of its Intranet services
business, but to a lesser extent than in previous years, both in terms of
dollars and as a percentage of the Company's total net revenue.
 
     Net revenue increased 158% from $12.0 million for the nine months ended
September 30, 1996 to $30.9 million for the nine months ended September 30,
1997. This increase in net revenue was primarily attributable to the increase in
the number of domain name subscriptions, principally in the .com TLD. Net
revenue from registration services increased 318% from $6.2 million for the nine
months ended September 30, 1996 to $25.9 million for the nine months ended
September 30, 1997. The provision for uncollectible accounts used in determining
net registration revenue for the nine months ended September 30, 1996 and 1997
was consistently applied at a rate of 30%.
 
     Net registrations increased 136% from 284,000 for the nine months ended
September 30, 1996 to 669,000 for the nine months ended September 30, 1997.
 
     Net revenue from Intranet services decreased 14% from $5.8 million for the
nine months ended September 30, 1996 to $5.0 million for the nine months ended
September 30, 1997. The decrease was attributable to a reduction in business
from NationsBanc which accounted for $2.7 million for the nine months ended
September 30, 1996 and $1.7 million for the nine months ended September 30,
1997. The
 
                                        9
<PAGE>   10
 
remaining Intranet services business experienced growth for the nine months
ended September 30, 1997, primarily through leveraging opportunities with SAIC
customers.
 
     Cost of Revenue.  Cost of revenue consists primarily of salaries and
employee benefits, fees paid to subcontractors for work performed in connection
with projects, depreciation, lease costs of the operations infrastructure and
the associated operating overhead. Cost of revenue increased 89% from $3.7
million for the three months ended September 30, 1996 to $7.0 million for the
three months ended September 30, 1997. The increase was primarily driven by the
growth of the Company's registration business which experienced additional labor
costs of $1.4 million and additional outsourcing costs of
$1.1 million to vendors in support of the Company's invoicing, collection and
processing activities. The Company continues to invest in improvements to the
back office component of its domain name registration business including
investments in additional hardware, software, staffing and facilities and
currently anticipates that it will continue to make significant investments in
its back office for the foreseeable future. In June 1997, the Company opened a
31,000 square foot facility to support its Internet business operations. This
leased facility is designed to meet current registration services customer
support needs as well as to provide expansion capacity for future business.
 
     As a percentage of net revenue, cost of revenue decreased from 71.8% for
the three months ended September 30, 1996 to 57.8% for the three months ended
September 30, 1997. This decrease primarily reflects economies of scale that the
Company has begun to achieve due to the growth of its subscription-based domain
name registration business. In the near term, the continued need for back office
investments is expected to partially offset future margin improvements arising
from economies of scale.
 
     Cost of revenue increased 81% from $10.2 million for the nine months ended
September 30, 1996 to $18.5 million for the nine months ended September 30,
1997. This increase was driven by $5.0 million in additional labor costs
primarily associated with supporting the growth of the Company's registration
services business.
 
     As a percentage of net revenue, cost of revenue decreased from 85.3% for
the nine months ended September 30, 1996 to 59.8% for the nine months ended
September 30, 1997.
 
     Research and Development Expenses.  Research and development expenses
consist primarily of compensation expenses to support the development and
enhancement of the Company's technologies. Research and development expenses
increased 67% from $226,000 for the three months ended September 30, 1996 to
$377,000 for the three months ended September 30, 1997. To date, all of the
Company's development costs have been expensed as incurred. The Company expects
that the level of research and development expenses will increase significantly
in the near future in absolute dollars as the Company invests in new product and
service offerings. As a percentage of net revenue, research and development
expenses decreased from 4.4% for the three months ended September 30, 1996 to
3.1% for the three months ended September 30, 1997.
 
     Research and development expenses increased 287% from $284,000 for the nine
months ended September 30, 1996 to $1.1 million for the nine months ended
September 30, 1997. As a percentage of net revenue, research and development
expenses increased from 2.4% for the three months ended September 30, 1996 to
3.5% for the three months ended September 30, 1997.
 
     Selling, General and Administrative Expenses.  Selling, general and
administrative expenses consist primarily of salaries of business development,
general management, administrative and financial personnel, corporate services
from SAIC, legal costs and amortization of goodwill associated with the
Company's acquisition by SAIC. Selling, general and administrative expenses
increased 63% from $1.9 million for the three months ended September 30, 1996 to
$3.1 million for the three months ended September 30, 1997. The increase was
attributable to increased management and administrative labor and an increase in
legal costs associated with the administration of the Company's domain dispute
policy. These expenses include $263,000 of expenses allocated from SAIC during
the three months
 
                                       10
<PAGE>   11
 
ended September 30, 1996 and $304,000 of expenses which were charged by SAIC
during the three months ended September 30, 1997.
 
     As a percentage of net revenue, selling, general and administrative
expenses decreased from 37.3% for the three months ended September 30, 1996 to
25.5% for the three months ended September 30, 1997. The decrease in percentage
of net revenue reflects economies the Company has begun to achieve due primarily
to the growth of its domain name registration business. The Company expects that
the level of selling, general and administrative expenses will increase
significantly in the near future in terms of absolute dollars as operations
continue to expand.
 
     Selling, general and administrative expenses increased 84% from $4.3
million for the nine months ended September 30, 1996 to $7.9 million for the
nine months ended September 30, 1997. The increase was attributable to increased
management and administrative labor of $1.7 million and an increase in legal
costs of $405,000 associated with the administration of the Company's domain
dispute policy. These expenses include $588,000 of expenses allocated from SAIC
during the nine months ended September 30, 1996 and $770,000 of expenses which
were charged by SAIC during the nine months ended September 30, 1997.
 
     As a percentage of net revenue, selling, general and administrative
expenses decreased from 35.8% for the nine months ended September 30, 1996 to
25.6% for the nine months ended September 30, 1997. The decrease in percentage
of net revenue reflects economies the Company has begun to achieve due primarily
to the growth of its domain name registration business. The Company expects that
the level of selling, general and administrative expenses will increase
significantly in the near future in terms of absolute dollars as operations
continue to expand.
 
     Interest Income.  The Company had net interest income of $288,000 for the
three months ended September 30, 1996 as compared to $570,000 for the three
months ended September 30, 1997.
 
     The Company had net interest income of $374,000 for the nine months ended
September 30, 1996 as compared to $1.1 million for the nine months ended
September 30, 1997. The change for both the three month and nine month
comparisons is attributable to increased cash flow associated with the Company's
registration services business.
 
     Income Taxes (Benefit).  The income tax benefit was $116,000 for the three
months ended September 30, 1996 as compared to an income tax expense of $995,000
for the three months ended September 30, 1997. The effective tax rate changed
from 28% for the three months ended September 30, 1996 to 45% for the three
months ended September 30, 1997.
 
     The income tax benefit was $692,000 for the nine months ended September 30,
1996 as compared to an income tax expense of $2,006,000 for the nine months
ended September 30, 1997. The effective tax rate changed from 28% for the nine
months ended September 30, 1996 to 45% for the nine months ended September 30,
1997. The difference between the effective rates for both the three month and
nine month comparisons is principally attributable to the relative impact that
non-deductible goodwill had on pretax operating income or loss for the quarter.
The goodwill amount is being amortized by the Company over five years and is
associated with the acquisition of the Company by SAIC in 1995.
 
LIQUIDITY AND CAPITAL RESOURCES
 
     From its acquisition by SAIC in March 1995 until December 1996, the Company
participated in SAIC's centralized cash management system whereby cash received
from operations was transferred to SAIC's centralized cash accounts and cash
disbursements were funded from such centralized cash accounts. Accordingly, cash
requirements for operating purposes and for capital expenditures were met from
this source. Beginning in 1997, the Company implemented its own cash management
system.
 
     At September 30, 1997, the Company's cumulative net obligation to SAIC for
intercompany activity was $21.9 million, an increase of $6.6 million for the
nine months then ended. Intercompany activity is primarily comprised of
corporate income tax payments made by SAIC on behalf of the
 
                                       11
<PAGE>   12
 
Company in accordance with the companies' tax sharing arrangement and salaries
and benefits paid by SAIC on behalf of the Company. Effective with the second
quarter of 1997, corporate taxes were paid to SAIC on a quarterly basis, with
all other intercompany balances between SAIC and the Company paid on a monthly
basis. Pursuant to the Tax Sharing Agreement dated September 26, 1997, the
Company will now remit income tax payments directly to tax authorities as it no
longer is part of SAIC's consolidated group for tax purposes.
 
     The Company completed its initial public offering on October 1, 1997
raising $54 million for the Company. From these proceeds, the Company paid the
$10 million dividend to SAIC on October 1, 1997. In addition, the Company made
its quarterly tax and intercompany activity payments to SAIC totaling $10.5
million by October 3, 1997 with the remaining $11.4 million to be paid by
November 15, 1997.
 
     Cash provided by operations was $26.5 million for the nine months ended
September 30, 1997. This amount is principally attributed to net income plus the
increase in deferred revenue reflecting cash collected in advance of revenue
recognition ratably over the 24- and 12-month registration periods. Partially
offsetting this amount is an increase in deferred tax assets resulting from
accelerated revenue recognition for tax purposes and the subsequent tax
liabilities.
 
     Investing activities used $29.6 million for the nine months ended September
30, 1997 of which $28.3 million was net purchases of short-term investments,
primarily commercial short-term investment grade securities. Purchases of
furniture and equipment of $1.2 million for the period represents a decrease
from the nine months ended September 30, 1996 as a result of the utilization of
lease arrangements during 1997. The majority of capital acquisitions are to
support growth in the domain name registration business and are expected to
continue to be financed under lease agreements ranging from 24 to 36 months.
 
     The Company believes that the net proceeds from its IPO, combined with its
existing cash balance, short-term investments and cash flows expected from
future operations, will be sufficient to meet the Company's capital requirements
for at least the next 18 to 24 months.
 
ITEM 3. QUANTITATIVE AND QUALITATIVE DISCLOSURES ABOUT MARKET RISK.
 
     Not Applicable.
 
PART II OTHER INFORMATION
 
ITEM 1. LEGAL PROCEEDINGS.
 
     As of October 31, 1997, the Company was a defendant in nine lawsuits
involving domain name disputes between trademark owners and domain name holders.
The Company is drawn into such disputes, in part, as a result of claims by
trademark owners that the Company is legally required, upon request by a
trademark owner, to terminate the right the Company granted to an alleged
trademark infringer to register the domain name in question. Further, trademark
owners have also alleged that the Company should be required to monitor future
domain name registrations and reject registrations of domain names which are
identical or similar to their federally registered trademark. The holders of the
domain name registrations in dispute have, in turn, questioned the Company's
right, absent a court order, to take any action which suspends their
registration or use of the domain names in question. Such litigation has
resulted in, and any future litigation can be expected to result in, substantial
legal and other expenses to the Company and a diversion of the efforts of the
Company's personnel.
 
     On June 27, 1997, SAIC received a Civil Investigative Demand ("CID") from
the U.S. Department of Justice ("DOJ") issued in connection with an
investigation to determine whether there is, has been, or may be a violation of
antitrust laws under the Sherman Act relating to Internet registration products
and services. The CID seeks documents and information from SAIC and the Company
relating to their Internet registration business. The Company is in the process
of producing the documents and
 
                                       12
<PAGE>   13
 
information requested. Neither SAIC nor the Company is aware of the scope or
nature of the investigation. The Company cannot reasonably estimate the
potential impact of the investigation or can it predict whether a civil action
will ultimately be filed by the DOJ or by private litigants as a result of the
DOJ investigation or, if filed, what such action would entail. The Company is
unable to predict the form of relief that might be sought in such an action or
that might be awarded by a court or imposed as a result of any settlement
between the Company and the DOJ or private litigants. Any such relief could have
a material adverse effect on the Company's business, financial condition and
results of operations.
 
     On March 20, 1997, PG Media, Inc., a New York-based corporation ("PG
Media"), filed a lawsuit against the Company in the United States District
Court, Southern District of New York alleging that the Company restricted access
to the Internet by not adding TLDs in violation of the Sherman Act. In its
complaint, PG Media has, in addition to requesting damages, asked that the
Company be ordered to amend the root zone configuration file so that the file
includes reference to PG Media's TLDs and nameservers. The Company has answered
the complaint. In addition, the Company recently received written direction from
the National Science Foundation ("NSF") not to take any action to create
additional TLDs or to add any new TLDs to the Internet root servers until
further guidance is provided by the NSF. On September 17, 1997, PG Media filed a
Second Amended Complaint adding the NSF as a defendant. The Company believes
that it has meritorious defenses and intends to vigorously defend itself against
the claims of PG Media. While the Company cannot reasonably estimate the
potential impact of such claims, a successful claim under the plaintiff's theory
could have a material adverse effect on the Company's business, financial
condition and results of operations.
 
     On October 17, 1997, a group of six plaintiffs filed a lawsuit against the
Company and the NSF in the United States District Court, District of Columbia,
alleging violations of the Competition in Contracting Act, the Sherman Act and
the Fifth Amendment. Relief sought includes restitution of fees collected from
domain name registrants, damages, injunctive and other relief. The Company
believes that it has meritorious defenses and intends to vigorously defend
itself against these claims. While the Company cannot reasonably estimate the
potential impact of such claims, a successful claim under the plaintiffs' theory
could have a material adverse effect on the Company's business, financial
condition and results of operations.
 
     The Company is involved in various other investigations, claims and
lawsuits arising in the normal conduct of its business, none of which, in the
opinion of the Company's management, will have a material adverse effect on its
consolidated financial position, results of operations, cash flows or its
ability to conduct business.
 
ITEM 2. CHANGES IN SECURITIES AND USE OF PROCEEDS.
 
     The Company's Registration Statement on Form S-1 (Registration No.
333-30705) was declared effective September 25, 1997 by the Securities and
Exchange Commission. The managing underwriters of the Class A Common Stock
offering commencing September 26, 1997 were Hambrecht & Quist, J.P. Morgan & Co.
and PaineWebber Incorporated. The Company registered and sold 3,220,000 shares
for its own account at an aggregate price of $57,960,000 and the selling
stockholder (SAIC) registered and sold 575,000 shares for its account at an
aggregate price of $10,350,000, for a combined total of 3,795,000 shares at an
aggregate price of $68,310,000. The offering has since terminated.
 
     The total amount of expenses incurred for the Company's account in
connection with the offering is estimated at $5,457,200, which is comprised of
$4,057,200 for underwriting discounts and commissions and $1,400,000 of other
expenses. No expenses were paid to directors, officers or persons owning more
than ten percent of any class of the Company's equity securities. The resultant
Company's net offering proceeds were $52,502,800. The net proceeds to SAIC for
its account were $9,625,500 after deducting the associated underwriting
discounts and commissions of $724,500.
 
     As of September 30, 1997, the Company had not received the proceeds from
the offering. On October 1, 1997, the Company received the offering proceeds
from which the $10,000,000 dividend was
 
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<PAGE>   14
 
paid to SAIC. SAIC owns ten percent or more of a class of the Company's equity
securities and is an affiliate of the Company. The remaining proceeds have been
invested in short-term investment grade government discount notes and commercial
paper.
 
ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K.
 
     (a) Exhibits -- See Exhibit Index
 
     (b) Reports on Form 8-K:
        None
 
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<PAGE>   15
 
                                   SIGNATURE
 
     Pursuant to the requirements of the Securities Exchange Act of 1934, the
registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.
 
                                          NETWORK SOLUTIONS, INC.
 
Date: November 14, 1997                   BY   /s/ ROBERT J. KORZENIEWSKI
                                            ------------------------------------
                                                   Robert J. Korzeniewski
                                                  Chief Financial Officer
 
                                       15
<PAGE>   16
 
                                 EXHIBIT INDEX
 
                            NETWORK SOLUTIONS, INC.
                        QUARTER ENDED SEPTEMBER 30, 1997
 
<TABLE>
<CAPTION>
EXHIBIT                                                                                 SEQUENTIAL
  NO.                               DESCRIPTION OF EXHIBITS                              PAGE NO.
--------   --------------------------------------------------------------------------   ----------
<S>        <C>                                                                          <C>
3(i)*      Second Amended and Restated Certificate of Incorporation..................
3(ii)*     Bylaws of the Registrant, as amended......................................
4.1*       Form of Common Stock Certificate..........................................
4.2        Reference is made to Exhibits 3(i) and 3(ii)..............................
27.1       Financial Data Schedule...................................................
11         Statement of Computation of Pro Forma Net Income (Loss) Per Share
             (Unaudited).............................................................        17
</TABLE>
 
---------------
* Incorporated by reference to exhibit of the same number to the Registrant's
  Registration Statement on Form S-1 (Registration No. 333-30705), originally
  filed with the Securities and Exchange Commission on July 3, 1997.
 
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